Question: Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), $x$ seconds after Amir threw it, is modeled by $h(x)=-(x+1)(x-7)$ How many seconds after being thrown will the ball reach its maximum height?
Explanation: The ball's height is modeled by a quadratic function, whose graph is a parabola. The maximum height is reached at the vertex. So in order to find when that happens, we need to find the vertex's $x$ -coordinate. The vertex's $x$ -coordinate is the average of the two zeros, so let's find those first. $\begin{aligned} h(x)&=0 \\\\ -(x+1)(x-7)&=0 \\\\ \swarrow &\searrow \\\\ x+1=0\text{ or }&x-7=0 \\\\ x={-1}\text{ or }&x={7} \end{aligned}$ Now let's take the zeros' average: $\dfrac{({-1})+({7})}{2}=\dfrac62=3$ In conclusion, the ball will reach its maximum height $3$ seconds after it is thrown.